Stability of polytopes of matrices via affine parameter-dependent lyapunov functions : Asymptotically exact LMI conditions

By Ricardo C. L. F. Oliveira, Pedro Luis Dias Peres. 2005

167 citations recorded by the source corpus.

Abstract This paper investigates necessary and sufficient conditions for the existence of an affine parameter-dependent Lyapunov function assuring the Hurwitz (or Schur) stability of a polytope of matrices. A systematic procedure for constructing a family of linear matrix inequalities conditions of increasing precision is given. At each step, a set of linear matrix inequalities provides sufficient conditions for the existence of the affine parameter-dependent Lyapunov function. Necessity is asymptotically attained through a relaxation based on a generalization of Polya’s Theorem to the case of matrix valued functions. Numerical experiments illustrate the results.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7f63ced9b64ac2f0f5d59468a37a9dd1ead2554e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Ricardo C. L. F. Oliveira
2. Pedro Luis Dias Peres

In Control and Systems Engineering

1. Ricardo C. L. F. Oliveira
2. Pedro Luis Dias Peres
3. Graziano Chesi

In Numerical Analysis

1. Ricardo C. L. F. Oliveira
2. Pedro Luis Dias Peres
3. Graziano Chesi

Citations in the corpus

• Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations (2007, methodology): “The results exploit the generalization of the Pólya’s theorem for the case of positive polynomials with matrix-valued coefficients [16]–[18].”